A negative result won't make a career. I don't think there's much danger when requiring negative results going onto a repository of over incentivising negative results. You can't mandate Nature or Cell publishes negative results.

    we tried using 0.10 mL, it didn't work
    we tried using 0.11 mL, it didn't work
    we tried using 0.13 mL, it didn't work
    we tried using 0.15 mL, it didn't work
    we tried using 0.17 mL, it didn't work
    we tried using 0.16 mL, it didn't work
    we tried using 0.18 mL, it didn't work
    we tried using 0.20 mL, it didn't work
    we tried using 0.14 mL, it didn't work
    we tried using 0.12 mL, it worked so we published

Do you want to know the ones that "didn't work" existed? Or are you happy with just the one that "worked" being written up in isolation?

If someone really tested those hypotheses, let them publish. I doubt they'll get funding so it'll be on their own dime. In practice people do run experiments like that, but they only publish the 1/4 trials that is successful.

Look to physics for how negative results should be published. There typically has to be reason to suspect some dosage range should work, in which case that sequence of studies you describe would be perfectly valid if it's within that range.